The technique I describe in the article strictly interpolates between known positions; it never extrapolates further, so other players would never be seen or rendered beyond the point where they actually stopped.
Yes, I got this. Just wanted to point out that a particular consequence of extrapolating would be that players can see enemys around corners. You already mention that the game would be unplayable if players get teleported every few ms, and above just describes why, aside from aesthetics, makes it unplayable.